I'm playing a Red Dragonborn Abjurer, and just got the Spell Resistance trait, so I have both resistance against all damage from spells and resistance specifically to fire damage. If I were hit by a spell dealing fire damage, would I take one half or one fourth damage?

Thanks in advance

I am pretty sure it is 1/2. Resistances do not stack. However, this does mean that you can fall into non-magical lava just as safely as magical lava!

In your example you would still take half damage. If you saved against fire dragon breath then you could take 1/4 damage in this case because it is a damage reduction that is different than resistance. Hilariously in that circumstance, if the dragon dealt 7 fire damage, you would only take 1 because you round down twice.

Resistance is a game effect that explicitly doesn't stack, even if the effects granting the resistance are different:

From Basic Rules:

Multiple instances of resistance or vulnerability that affect the same damage type count as only one instance. For example, if a creature has resistance to fire damage as well as resistance to all nonmagical damage, the damage of a nonmagical fire is reduced by half against the creature, not reduced by three-quarters.